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Abstract

Many species of butterflies exhibit interesting optical phenomena due to structural color. The physical reason for this color is subwavelength features on the surface of a single scale. The exposed surface of a scale is covered with a ridge structure. The fully three-dimensional, periodic, finite-difference time- domain method is used to create a detailed electromagnetic model of a generic ridge. A novel method for presenting the three-dimensional observed color pattern is developed. Using these tools, the change in color that is a result of varying individual features of the scale is explored. Computational models are developed that are similar to three butterflies: Morpho rhetenor, Troides magellanus, and Ancyluris meliboeus.

Computational model. (a) Portion of a scale showing three ridges. The volume within the black frame is the volume used for the periodic FDTD calculations. (b) Detail of a single ridge showing the individual FDTD cells. (c) Arrangement of the electromagnetic field components within a single FDTD cell.

Comparison of results from an ensemble average of randomized finite models and a periodic model. (a) Far-zone scattering pattern for the ensemble average of 100 simulations with 50 randomly spaced ridges per simulation. (b) Far-zone scattering pattern for the periodic model. (c) Comparison of the reflection coefficients for the ensemble average and the periodic model.

Observed color as a function of direction for Morpho-like models. For all cases, there are eight lamellae and a base. (a) Aligned lamellae without taper, Ymax=1.0. (b) Aligned lamellae with the top four lamellae tapered, Ymax=0.30. (c) Aligned, tapered lamellae plus a cover scale (dielectric slab), Ymax=0.28. (d)–(f) Same as (a)–(c), but with offset lamellae. (d) Ymax⁡=0.21. (e) Ymax⁡=0.05. (f) Ymax⁡=0.22.

Far-zone scattering patterns for the Morpho model shown in Fig. 9a. (a) Pattern in the y–z plane. (b) Pattern in a perpendicular plane that passes through the peak of the beam (angle measured from θ=20°, ϕ=90°).

Observed color as a function of direction for Morpho-like models that include microribs. For both cases, there are eight lamellae with the top four lamellae tapered and a base: (a) aligned lamellae, Ymax=0.26; (b) offset lamellae, Ymax=0.05.

Photographs of the dorsal side of a male Troides magellanus butterfly. In both views, the light source is located near the observation point. (a) From most observation directions, the observed color of the lower wings is yellow. (b) When illuminated and viewed near grazing, the color of the lower wings changes abruptly, with a change in angle, to blue.

Observed color as a function of direction for Troides magellanus model with six aligned lamellae. The details for the model are the same for all cases, and only the direction of the incident light is changed: (a) θi=40°, Ymax=0.05; (b) θi=50°, Ymax=0.14; (c) θi=70°, Ymax=1.0.